Math 015 Section 6.4 Translating Equations. Translating Sentences into Equations An equation states...

Math 015 Section 6.4 Translating Equations

Translating Sentences into Equations

An equation states that two mathematical expressions are equal

To translate a sentence into an equation requires recognition of the words or phrases that mean “equals”

equals is is equal to amounts to represents

=

Once the sentence is translated into an equation, the equation can be solved by rewriting into a form using variables and constants.

Example: Sentence: five less than a number is thirteen

Equation: five less than a number = thirteen

n – 5 = 13

n = 18

Assigning variable expressions

Problem: Eight less than three times a number equals five times the number. Find the number.

Let: x = the number Assigning variables to the things involved in the problem should be shown as part of your work.

8 less than 3 times a number = 5 times the number

3x – 8

-8 = 2x

-4 = x Answer:

The number is -4

= 5x

Problem: Translate “four more than five times a number is six less than three times the number” into an equation and then solve the equation.

Answer: The number is -5

Let: x = the number

4 more than 5 times a number = 6 less than 3 times the number

5x + 4

5x = 3x – 10

2x = -10

= 3x – 6

x = -5

Problem: Six hundred thousand of the first-year students at U.S. colleges are taking at least one remedial class in reading, writing, or mathematics. This is three-tenths of the total number of first-year students. How many first year students are in U.S. colleges.

600,000 is 3/10 of the first year students

600,000

6,000,000 = 3x

2,000,000 = x

Answer: There are 2,000,000 first-year students at U.S. Colleges

Let: x = the number of 1st year students.

= x 3 10

10

Problem: A wallpaper hanger charges $50 plus $28 per roll of wallpaper used in a room. If the total charge for hanging wallpaper in a room is $218, how many rolls of wallpaper were used in that room?

Let: x = # of rolls of wallpaper uses

Price $28 times the # of rolls = $50

168 = 28x

Answer: 6 rolls of wallpaper were used for theroom.

+

218 = 50 + 28x

6 = x

Problem: A board that is 20 ft long is cut into two pieces. Five times the length of the shorter piece is 2 ft more than twice the length of the longer piece. Find the length of each piece.

20 ft

x (20 – x)

5x

5x = 40 – 2x + 2

5x = -2x + 42

7x = 42

x = 6

Answer: Shorter piece = 6 ft Longer piece = 14 ft

5 times the short piece

= 2 times the long piece

+ two

Let: x = short piece

20 – x = long piece

= 2(20 – x) + 2

Problem: The sum of two numbers is 9. Eight times the smaller numbers is five less than three times the larger number. Find the two numbers.

8 times the small # = 5 less than 3 times the larger #

Answer: The smaller number is 2

The larger number is 7

Let: x = the smaller number

9 – x = the larger number

8x = 3(9 – x) – 5

8x = 27 – 3x – 5

8x = -3x + 22

11x = 22

x = 2